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I think the child would be a half-blood, because if a Muggle knows how to do magic, it means that somebody in their distant family knew magic and it must've skipped a few generations. Therefore the Muggle has some magical blood in them.

Yes, and even if their children married purebloods, and their grandchildren married purebloods, they'd be considered "halfbloods". I don't think any of them are considered "purebloods" until the fifth generation and even then, amongst a great deal of the Wizarding World (Blacks, Malfoys), they aren't given that distinction.

You're only considered a Pureblood if your grandparents were all magical.

So Harry is a Half-Blood because his mother was a Muggleborn, so half of his grandparents are Muggles, but his children with Ginny are all Pureblood because Lily, James, Molly, and Arthur are all magical.

It seems like a wizard really concerned about blood status would consider the child of a muggleborn and a muggle to be a "mudblood", not a halfblood. I guess it depends on whose perspective this is from. Blood status really seems to be all relative.

The children of a Muggleborn and a Muggle would have no magical grandparents. However, what could you call them? You couldn't really call them a Muggleborn, because that gives the impression that their parents were both Muggles. Mudblood, of course, is only used by those to who blood matters.

So if this person was being referred to by a person to whom blood didn't matter, they would be most likely be called a half-blood. Of course, if blood status doesn't matter to the person that is doing the labelling it is unlikely they would refer to someone by their blood status anyway.